"Trump canceled a planned trip with Nielsen this week to visit US troops at the border in South Texas and told aides over the weekend he wants her out as soon as possible", The Washington Post reported, citing five current and former White House officials.
According to U.S. media, Ms Ricardel had a recent spat with members of the first lady's staff over her trip to Africa, including seating on the plane and use of National Security Council resources.
During a panel discussion Tuesday, host Jake Tapper cited a Wall Street Journal report that revealed the only people who feel secure in their jobs at the White House are related to the president.
A spokesman for the National Security Council had no immediate comment.
Ricardel is the deputy to national security adviser John Bolton.
One of the sources said that their dealings over the trip "didn't go well".
Earlier Tuesday, Ricardel participated in a celebration at the White House celebrating the Indian Diwali festival where Trump spoke.
Per multiple reports, there have been suspicions that Ricardel was behind some negative stories about the First Lady and there was an apparent clash between her and Melania Trump's staff over FLOTUS' recent trip to Africa.
Mr Trump cancelled a planned trip with Ms Nielsen this week to visit USA troops at the border in south Texas and told aides over the weekend he wants her out as soon as possible, these officials said.
Trump has been mulling removing Nielsen, a Kelly protege who became the secretary at Homeland Security when he left the job to become Trump's chief of staff, for a number of weeks, a source told Reuters news agency.
According to people familiar with the situation, Trump is also discussing replacing Kelly with Vice President Mike Pence's chief of staff, Nick Ayers. White House press secretary Sarah Sanders had no immediate reaction to Melania Trump's statement. One source familiar with the situation said Ricardel's firing is due in part to her "bullying" of aides both above and below her.
The report comes less than a week after Trump ousted Attorney General Jeff Sessions.
Nielsen had previously been Kelly's deputy, and kicking her to the curb could be a way for Trump to rid himself of Kelly too.